What is the 12th Fibonacci number?
The 12th term of the Fibonacci sequence is 89.
Answer and Explanation:
The 12th term of the Fibonacci sequence is 144, so the 12th Fibonacci number is 144. Alternatively, Binet's formula gives an expression for the nth Fibonacci number which depends only on n:Fn=(1+√52)n−(1−√52)n√5⟹F12=(1+√52)12−(1−√52)12√5=144.
| Sequence in the sequence | Resulting Fibonacci number (the sum of the two numbers before it) | Ratio of each number to the one before it (this estimates phi) |
|---|---|---|
| 12 | 144 | 1.617977528089888 |
| 13 | 233 | 1.618055555555556 |
| 14 | 377 | 1.618025751072961 |
| 15 | 610 | 1.618037135278515 |
...
12 (number)
| ← 11 12 13 → | |
|---|---|
| Cardinal | twelve |
| Ordinal | 12th (twelfth) |
| Factorization | 22× 3 |
| Greek numeral | ΙΒ´ |
How To Find The Nth Term of an Arithmetic Sequence - YouTube
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946, 17711, 28657, 46368, 75025, 121393, 196418, 317811, ... Can you figure out the next few numbers?
Fibonacci series is the series with the 1st and 2nd term as 1, and the all the further terms obtained by adding the previous 2 terms. So, the series turns out be : 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233 ...... As per the series, the 11th Fibonacci number is 89.
Mathematics - Fibonacci Sequence and the Golden Ratio - YouTube
We have only defined the nth Fibonacci number in terms of the two before it: the n-th Fibonacci number is the sum of the (n-1)th and the (n-2)th. So to calculate the 100th Fibonacci number, for instance, we need to compute all the 99 values before it first - quite a task, even with a calculator!
What is the sum of the first 12 terms of the Fibonacci sequence?
For example, the sum of the first 12 terms in a Fibonacci sequence is Σi=011 Fi = F13 -1 = 233 -1 = 232. If we add the first 12 terms manually, we get 0 + 1 + 1 + 2 + 3 + 5 + 8 + 13 + 21 + 34 + 55 + 89 = 232, we got the same thing as formula.
Fibonacci series is the series with the 1st and 2nd term as 1, and the all the further terms obtained by adding the previous 2 terms. So, the series turns out be : 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233 ...... As per the series, the 11th Fibonacci number is 89.
The first 12 terms of the fibonacci sequence are:1,1,2,3,5,8,13,21,34,55,89,144.